Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+6y &= 8 \\ 6x-8y &= -7\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = -6x-7$ Divide both sides by $-8$ to isolate $y$ $y = {\dfrac{3}{4}x + \dfrac{7}{8}}$ Substitute this expression for $y$ in the first equation. $-4x+6({\dfrac{3}{4}x + \dfrac{7}{8}}) = 8$ $-4x + \dfrac{9}{2}x + \dfrac{21}{4} = 8$ Simplify by combining terms, then solve for $x$ $\dfrac{1}{2}x + \dfrac{21}{4} = 8$ $\dfrac{1}{2}x = \dfrac{11}{4}$ $x = \dfrac{11}{2}$ Substitute $\dfrac{11}{2}$ for $x$ back into the top equation. $-4( \dfrac{11}{2})+6y = 8$ $-22+6y = 8$ $6y = 30$ $y = 5$ The solution is $\enspace x = \dfrac{11}{2}, \enspace y = 5$.